The rapid and effective generation of random number sequences is one of the grand challenges of modern computation. These sequences are used as keys for secure communications, as orderings for random sampling in simulations and data analysis, and are an important part of trustworthy gaming and lotteries. Devices that use random numbers are ubiquitous and as the spread of modern technology grows, so does the number of technologies that use them.
Nearly every online bank transaction, secure communication between governments and their embassies, signal from command & control centers to troops and aircraft, and large-scale computer simulation relies on these sequences. Hardware in supercomputers, personal computers, smart phones like iPhones™ and Blackberrys™, and military encryption devices all implement random number generators in some form.
Traditional methods for generating random numbers rely on deterministic algorithms or deterministic physical processes. Although these algorithms are deterministic, they are designed to produce numbers that satisfy certain characteristics that give the appearance of being random. For example, the digits of pi can be used as random numbers, but they are deterministically calculable and hence unsuitable for a cryptographic key, because if an adversary determines the algorithm used, the process is compromised. There is no traditional computational method for generating random numbers that is not deterministic. Therefore traditional techniques are vulnerable to compromise. Computationally generated random numbers are often called pseudo-random numbers for these reasons.
Since all classical algorithms are deterministic, the only way to generate truly random numbers is to utilize a suitable random physical effect. Quantum mechanical systems are the only known entities that have nondeterministic behaviour. While the evolution of the quantum mechanical probability distribution is deterministic, the outcome of a particular measurement is not. If the uncertainty of a measurement outcome can be mapped to a sequence of numbers, it can be used as a source of random number generation. This quantum noise is not simply due to lack of knowledge of an observer, but is due to the very nature of physical reality. Random number generators based on quantum effects are called true random number generators. The use of quantum effects for random number generators is in its infancy and there are a small number of competing methods at present.
As an example of quantum random number generation, one of the current state-of-the-art methods (ID Quantique 2011) is to attenuate a conventional light source (less than one photon per unit time) and project that light on to a 50% beam splitter. The photon may be randomly transmitted or reflected. The two cases correspond to the generation of either a 1 or a 0.
Many state-of-the-art quantum random number generation methods, including the ID Quantique method (ID Quantique 2011), generate only one bit of information per measurement corresponding to one of two states in which a physical system can exist. To generate large or many random numbers therefore requires a large number of measurements, slowing the rate of random number generation.
Recently, a method for generating random numbers based on measuring phase noise of a single-mode laser has been developed (Qi 2009; Qi 2010). The phase noise of a laser is due to electric field fluctuations caused by spontaneous photon emission and results in linewidth broadening. This method involves continuous wave pumping at low intensity followed by measuring coherence decay. The continuous wave pumping is done at low intensity in order to minimize the relative effects of additional classical noises. This may be a challenging condition to maintain with stability.
There has also been recent work on using amplified spontaneous emission for fast physical random number generation (Williams 2010). This method involves measuring energy fluctuations in broadband, incoherent, unpolarized optical noise generated through amplified spontaneous emission (ASE) in an amplifier. Like the method of Qi (Qi 2009; Qi 2010) discussed above, this method uses continuous wave pumping to amplify the effect of the energy fluctuations into a measurable signal. Further, this method measures energy fluctuations rather than phase.
There has also been recent work on using polarization states of spontaneous parametric down-converted photons for generating random numbers (Suryadi 2010). One problem with such a method is that measurement of polarization states only provides a single random bit, which is like most state-of-the-art quantum random number generation methods. Thus, to generate large or many random numbers, a large number of measurements are required, slowing the rate of random number generation.
There remains a need for true random number generators that can generate random numbers more quickly and with easier detection using a simple process based on quantum effects of a physical system.